Solve Quadratic Equation: 3x²+12x+c=0

In summary, the conversation is about solving for the value of c in a quadratic equation with different numbers of real and complex solutions. The quadratic formula is used to find solutions, and for there to be only one real solution, the discriminant (D) must equal zero. The value of c is then determined by solving for it in the discriminant equation, which will likely not result in a prime number.
  • #1
PhantomTechnic
2
0
Hello I've been stuck on this test review question for a few days, and I can't figure it out. Can someone help out?
"3x²+12x+c=0, Find solutions for c, where there is 1 real solution, 2 real solutions, and 2 nonreal(complex) solutions"
 
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  • #2
Hello and welcome to MHB, PhantomTechnic! (Wave)

Let's review the quadratic formula:

Given the quadratic equation:

\(\displaystyle ax^2+bx+c=0\)

Then the solution is given by:

\(\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)

Now, looking at that formula, what condition do we need for there to be only 1 solution?
 
  • #3
MarkFL said:
Hello and welcome to MHB, PhantomTechnic! (Wave)

Let's review the quadratic formula:

Given the quadratic equation:

\(\displaystyle ax^2+bx+c=0\)

Then the solution is given by:

\(\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)

Now, looking at that formula, what condition do we need for there to be only 1 solution?
Wouldn't it be when it equals zero?
 
  • #4
PhantomTechnic said:
Wouldn't it be when it equals zero?

When what equals zero? You are headed in the right direction, but I want to make certain you are talking about the correct expression...D
 
  • #5
To answer Mark, D = 12² - 4(3)c, where D is the discriminant. What equals 0?
Solve for c. What do you get? It's probably not a prime number!
 

FAQ: Solve Quadratic Equation: 3x²+12x+c=0

What is a quadratic equation?

A quadratic equation is a mathematical expression that contains a variable raised to the second power, also known as a squared term. It is in the form of ax²+bx+c=0, where a, b, and c are constants and x is the variable.

How do you solve a quadratic equation?

There are multiple methods to solve a quadratic equation, but the most common one is by using the quadratic formula: x = (-b±√(b²-4ac))/2a. First, identify the values of a, b, and c in the equation. Then, plug them into the formula and simplify to find the solutions for x.

What does the discriminant tell us about a quadratic equation?

The discriminant, which is the expression inside the square root in the quadratic formula, tells us about the nature of the solutions for a quadratic equation. If the discriminant is positive, there will be two real solutions. If it is zero, there will be one real solution. And if it is negative, there will be no real solutions, only complex solutions.

Can you solve a quadratic equation if the constant term (c) is missing?

Yes, it is possible to solve a quadratic equation even if the constant term is missing. In this case, the equation will be in the form of ax²+bx=0. You can factor out the variable and solve for x, or use the quadratic formula with c=0.

Can a quadratic equation have more than two solutions?

No, a quadratic equation can have a maximum of two solutions. This is because a quadratic equation is a second-degree polynomial, which can have a maximum of two x-intercepts on a graph. However, if the solutions are repeated, then the equation will have only one solution.

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